Air resistance has a quadratic velocity dependence. Water resistance usually has

Question

Air resistance has a quadratic velocity dependence. Water resistance usually has a linear velocity dependence. Consider a bicycle on a road where air resistance is the dominant resistive force on it. Also consider a canoeist on a lake where water resistance is the most important resistive force. They are both getting tired at the same rate as they move. At the speeds they are both going, the force the canoeist exerts is 1.5 times as big as the force the cyclist exerts. The rate at which someone gets tired is proportional to the force they exert times the velocity at which they are going. Hint: To answer these questions you will have to consider ratios of things at the beginning to things at the end. If both people increase their speed by 50%, which of them will get tired faster? a. The bicyclist. b. The canoeist. c. They both get tired at the same rate. d. Not enough information is given to determine an answer. 7. Which person will be exerting the larger force at the 50% higher speed? a. The bicyclist. b. The canoeist. c. They have the same force. d. Not enough information is given to determine an answer.

Explanation / Answer

When at constant speed the only force they exert is to overcome the resistance.

Hence we have : Let initial speed of canoe by VC and Initial speed of cyclist be VY.
Hence we have FC*VC = FY*VY; It is also given FC = 1.5FY.
Hence VC = 2VY/3 .
Now if speed becomes 1.5 times(50% increase) : F 'Y = 1.52 FY ; F 'C = 1.5 FC

Hence by calculating rate of getting tired we have for canoe : 1.5FC *1.5VC = 1.52 FCVC
For cyclist : 1.52FY*1.5VY = 1.53 FYVY.

Hence as FC*VC = FY*VY : the cyclist getts tired faster.
Correct option is a .

Now As FC = 1.5FY ; F 'C = 1.52FY = F 'Y
Force by both is same.
Correct option is c

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.